He didn't claim that. He said, "Jesus isn’t known to exist," and that is correct, largely because what constitutes a historical Jesus is fluid, and just about any itinerant rabbi in the Levant 2000 years ago can be said to be Jesus. Who wouldn't qualify given the believer's propensity to make whatever he has fit with whatever he believes? Of course that was Jesus. Yeah, his name was actually Emmanuel, and he only had three disciples, two women, but that's him! It's metaphor, allegory. Unbelievers just don't possess the necessary skills to see that, what with not having the counsel of the Spirit. That's how it's done.
Nor would he be a lunatic for so claiming if he did, certainly no more than those who claim Jesus was resurrected.
Furthermore, it doesn't matter how much of the story of Jesus is fact or fiction if the supernatural aspects are not accepted. If this wasn't a deity or channeling a deity, what difference does it make who wrote those words? Somebody did. Once divinity is removed, the source becomes irrelevant, and the words have to be judged on their own merit, just like with Socrates. Was there a historic Socrates, or did Plato invent him as a literary device to speak through?
What difference would it make either way? What difference does it make if there was a historical Socrates. The words attributed to him stand or fall on their own with or without a historic Socrates, and really all other literature. What if Shakespeare was really two nuns? It wouldn't matter for the same reason that it doesn't matter if Jesus was myth (all invented) or legend (some historical truth mixed with fiction). The historicity of Jesus, Socrates, and Shakespeare are interesting subjects, but it doesn't matter what the verdict is. Just like with this post. It doesn't matter who I am. The words stand or fall on their own.
And if they don't? If there is no God and the prophets are only speaking as any of us might except speaking through the literary device of a deity, then the Bible is reduced to the same status as Jesus if there was no resurrection, and to deny it's divinity is to have concluded correctly. At this level, the scriptures fall apart. Without faith and a faith-based confirmation bias to read scripture through, there is nothing there of value to the humanist except to consider it as literature or a cultural phenomenon - secular studies also appropriate for studying the Iliad.